Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1240 conjugacy classes of subgroups; only the 363 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 363 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C42×C52 | C2 | semidirect |
| 3. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 4. #11717246 | C2 | semidirect |
| 5. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 6. #11717192 | C2 | semidirect |
| 7. C42×C5⋊D5 | C2 | semidirect |
| 8. C4×#6045 | C2 | semidirect |
| 12. #87900 | C4 | direct (N × H) |
| 30. C2×C4×C52 | C2×C4 | semidirect |
| 35. C22⋊(C5⋊D5) | C2×C4 | semidirect |
| 38. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 40. C4×C5⋊D5 | C2×C4 | semidirect |
| 41. #6045 | C2×C4 | semidirect |
| 43. C2×C42×C5 | D5 | semidirect |
| 58. C4×C52 | #41 | semidirect |
| 86. C2×C4×C5 | C4×D5 | semidirect |
| 105. C2×C42 | C5⋊D5 | semidirect |
| 106. C52 | C4×#41 | semidirect |
| 115. C4×C5 | #709 | semidirect |
| 149. C2×C4 | C4×C5⋊D5 | semidirect |
| 154. C5 | C4×#709 | semidirect |
| 165. C4 | #87900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C42×C52 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717246 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #11717192 | 2 |
| C42×C5⋊D5 | 2 |
| C4×#6045 | 2 |
| C4×#709 | 5 |